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Prove that : If (4.44)^x=(0.444)^y=1000,...

Prove that : If `(4.44)^x=(0.444)^y=1000`, then prove that `(1)/(x)-(1)/(y)=(1)/(3)`.

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The correct Answer is:
`(1)/(3)`
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CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. Rearrange according to the ascending values : 3^(1/2),4^(1/3),5^(1/4).

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  2. Rearrange according to the ascending values : 2^(18),3^(12),4^(24),5^(...

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  3. Prove that : If (4.44)^x=(0.444)^y=1000, then prove that (1)/(x)-(1)/(...

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  4. If (111.1)^x=(11.11)^y=(1.111)^z then prove that (1)/(x)-(2)/(y)+(1)/(...

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  5. If 2^a=3^b=6^(-c), then prove that (1)/(a)+(1)/(b)+(1)/(c )=0.

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  6. If x^a=y^b=z^c " and "y^3=zx, then prove that b(c+a)=3ca.

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  7. If 4^a=36^b =9^c, then prove that (b)/(a)+(b)/( c)=1.

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  8. If x^2=y^3, then prove that (x/y)^(3/2)+(y/x)^-(2/3)=x^(1/2)+y^(1/3).

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  9. If a^x=z^y" and "a^z=z^x, then prove that x^2 =yz.

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  10. If (x^(n^2))^n = (x^(2^n))^2, then show that root(n+1)(n^3)=2.

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  11. If x=(sqrt(2)+1)^(-1/3), then prove that (x-x^(-1))^3+3(x-x^(-1))+2=0.

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  12. If (y/z)^a (z/x)^b (x/y)^c=1, then prove that (y/z)^((1)/(b-c))=(z/x)^...

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  13. If a= xy^(p-1), b=xy^(q-1),c=xy^(r-1), then show that a^(q-r).b^(r-p)....

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  14. The angle of elevation of the sun, when the length of the shadow of a ...

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  15. If x=3^(1/3)+3^(-1/3), find the value of (3x^3-9x).

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  16. If x= 2^(2/3)+2^(1/3), find the value of (x^3-6x).

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  17. If x=1+3^(2/3)+3^(1/3), find the value of (x^3-3x^2-6x-4).

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  18. If x=2^(1/3)-2^(-1/3), find the value of (2x^2+6x).

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  19. Solve : 3^(2x)+9=10.3^x

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  20. Solve : 6^(2x+4)=3^(3x).2^(x+8)

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